All references to the Dalai Lama were edited out when it was broadcast in Asia. In some channels the Dalai Lama parts were replaced with Lisa, while other channels had the Dalai Lama parts just edited out, leaving the storyline "gaping" and "unfocused."
The title of the episode is a reference to the nursery rhyme Simple Simon. This is rather appropriate because the rhyme's first verse was about the title character meeting a pieman.
When Homer is watching the bacon commercial at the beginning, if you look closely you can see Ralph Wiggum riding the conveyor belt with the pigs.
Nichelle Nichols is animated with grey hair, just as she really looks; this is very different than how she looked in her appearances on Futurama, where her hair is black. Her former Star Trek co-star Leonard Nimoy was drawn with dark hair in his appearances in both shows, though in recent years the actor has greyed and grown a beard.
This is the second episode where Homer accidentally provides evidence of his alter-ego and denies it when asked only to reveal it to Springfield eventually. The first was The Computer Wore Menace Shoes.
It makes sense that this episode would have a superhero cough gag since it's a superhero episode.
Homer says "It's Cobblering Time" a pie pun, and a reference to The Thing's catchphrase "It's Clobbering Time."